A Sydney Marist priest has challenged sceptics of religious miracles, posting a $5000 bounty for anyone who can prove the Lourdes miracles he has investigated are fakes.

The Sydney Morning Herald today quotes Fr Paul Glynn as saying that while medical science might explain some cures attributed to the shrine in southern France, not every instance of miraculous healing.

Fr Glynn and his cousin Bill Dougherty, a former regional newspaper proprietor, have offered the $5000 reward from their own pockets.

Millions of pilgrims have flocked to Lourdes since 1858, when a French peasant girl, Bernadette Soubirous, said she had been visited by an apparition of the Virgin Mary.

The Church has since recognised 66 miracles at the site, the most recent in 1987. A medical tribunal set up to investigate claims of miracles describes about 6800 cases as medically inexplicable, Father Glynn said. He said the cases had not met the condition of a declared miracle.

Fr Glynn has interviewed four people and reviewed the case notes of a further 20. He is convinced of their authenticity.

"It can take 12 to 20 years before miracles are even accepted," he said. "There must be a proven physical disease where pre-existing medical conditions have been documented, the cure must be instantaneous ... and it must be complete and permanent.

"They must be prepared to be examined by a medical tribunal and return to Lourdes to be re-examined for several years after."

Fr Glynn yesterday announced the reward to parishioners of St Kevin's Church, Dee Why, on the city's northern beaches, in an attempt to convince non-believers of the power of faith.

To win, a recognised professor of medicine must review the case medical notes and be prepared to verify and identify an explicable reason for cure and long-term recovery.